On the Impossibility of Reducing the Surplus Approach to a Neoclassical ‘Special Case’

A Criticism of Hahn in a Solowian Context

Bibliographic Data

ID12229751
AuthorsEmiliano Brancaccio (0000-0001-7765-3892, University of Sannio, corresponding author)
Year2010
Volume22
Issue3
Pages405-418
Publication date2010-07-01
Peer ReviewedYes
Open AccessNo
TypeARTICLE
VenueReview of Political Economy (JOURNAL)
Journal identifiersISSN: 0953-8259 • E-ISSN: 1465-3982
PublisherTaylor & Francis (PUBLISHER • GB)
DOI10.1080/09538259.2010.491288
OpenAlexW1997512077
LanguageEN
Citations received4
References cited13

We propose a new criticism of Frank Hahn’s attempt to prove that the surplus approach constitutes no more than a ‘special case’ of the neoclassical model of intertemporal general equilibrium. In particular, we show that Hahn’s ‘special case’ is vitiated by the paradox of determining the past as a function of the future. In order to make the communication between schools of thought easier, we present our criticism of Hahn within a mathematical framework drawn from the well-known Solow growth model. Acknowledgment I am grateful to Roberto Ciccone and Ian Steedman for their helpful comments on a previous version of this paper. Notes 1Some economists have used the term ‘neo-Ricardian’ in a negative sense to call into question the connections between this approach and the work of Marx (see, for example, Rowthorn, Citation1974). However, the well-known differences between Sraffians and more traditional Marxists regarding the labour theory of value are not sufficient to deny the Marxian legacy of the surplus approach. 2For one thing, the mathematical system adopted will describe an economy that produces only one good and thus precludes any examination of Sraffa’s important criticism of the neoclassical theory of capital. For another, it envisages a continuous and differentiable production function with perfect substitutability of the factors of production, which has always been considered wholly unrealistic by Sraffian theorists. Moreover, it assumes constant returns to scale, which Sraffa specifically indicated as unnecessary for the purposes of his analysis. 3Some of these concepts had already been expressed by Hahn Citation(1975). See Bliss Citation(1975) for a similar approach. 4For these and other criticisms, see Duménil & Lévy Citation(1985), Garegnani (Citation1990, Citation2003), Kurz & Salvadori Citation(1995), Pasinetti Citation(2000), Petri Citation(2003), and Schefold Citation(1985). 5The point of reference is Hahn’s Equation 3.18. 6This theoretical structure coincides at the conceptual level with the one represented by Hahn’s Equations 3.17, 3.22 and 3.25. 7Some clarification is called for as regards the connection between non-stationary and short-period equilibrium, which involves a logical link between Solow’s analysis and the modern analyses of intertemporal and temporary equilibrium. Solow subjects the behaviour of agents to marked degree of simplification so as to eliminate problems regarding optimal intertemporal allocation and expectations. The temporal structure of the model is, however, analogous to its more complex counterpart in the modern analyses of neoclassical general equilibrium, and it is for this reason that we have been able to incorporate the operation carried out by Hahn within it. At the same time, it should be specified that the analogy between short-period equilibrium and non-stationary Solowian equilibrium is permissible because the model presented here has only one good and therefore treats capital as a homogeneous physical magnitude. If capital were instead expressed in terms of value, a point of non-stationary equilibrium with K given and a unique and uniform rate of profit would have to be regarded as a long-period equilibrium in the classical and traditional neoclassical sense of the term (Garegnani, Citation1976). The steady growth equilibrium of the Solow model would instead correspond in that case to an equilibrium described by classical and traditional neoclassical economists as ‘secular’ (see Garegnani, Citation1976; Petri, Citation1999). It should of course be borne in mind that with K expressed in terms of value, Solow’s model would be subject to the Sraffian criticisms of the neoclassical theory of capital. 8In formal terms, it is unquestionably possible to combine a Sraffian system of production prices with an equation of macroeconomic equilibrium. In particular, given the classical saving hypothesis and the assumption that the rate of growth is exogenous, it is possible to obtain the rate of profit from the macroeconomic equilibrium. Given the latter, it is then possible to arrive through the system of production prices at the determination of wages and the relations of exchange between goods. This solution has, however, been put forward only by some of Sraffa’s successors, and as Pasinetti Citation(1990) has noted, it constitutes only one of the various possible formal closures of a Sraffian system. Others have instead subjected this procedure to marked criticism based on the idea that Sraffa’s exogenous distributive variable—which can be the rate of profit or wages—refers to a ‘normal’ distribution in the classical sense, which is assumed to be characterised by a certain degree of ‘persistence’ and cannot therefore be regarded as directly dependent on the continuous change of macroeconomic variables. Critics have also pointed out that this procedure unduly restricts dynamic analysis of the quantities produced, confining it exclusively to the case of steady growth. They have therefore indicated alternative ways of restoring macroeconomic equilibrium that are based no longer on variations in the rate of profit but rather on change in the degree of utilisation of productive capacity or the amount of autonomous expenditure that does not generate additional capacity. See Brancaccio Citation(2003) for an overview and Brancaccio Citation(2008) for an analytical synthesis of these positions. 9The procedure that Hahn Citation(1982) encloses in the system of equations, Equations 3.22′ to 3.30, is thus presented within the framework of a model with a single good. 10In fact, Hahn (Citation1982, Section 5) uses this expression with reference to the problem of the uniformity of rates of profit rather than the compatibility between the rate of accumulation, rate of profit and optimal ratio of physical capital to labour. The terms of the problem are, however, completely equivalent at the conceptual level in the sense that Hahn’s expression refers in any case to what it he regards as the primary limitation of the Sraffian surplus analysis, namely an unavoidable—except by chance—incompatibility between the endowments and the other exogenous variables of the model. 11Hahn seems to realise the problem when he states that ‘there is an interpretation of [the growth rate] connected with the question of “animal spirits” which would cause difficulties to the neoclassical theory’. The issue is then hastily dismissed, with a remark to the effect that problems of interpretation are of no importance to the case considered (Hahn, Citation1982, p. 367). This is somewhat perplexing, as Hahn’s article is wholly concerned with putting forward a neoclassical interpretation of the surplus approach. 12This difference between the two approaches can also be shown within the framework of the Solowian system used here. Consider a case in which the technique k is fixed and exogenous. For the surplus approach, this hypothesis is in no way detrimental to the solution of the system. Prices and distributive variables can be determined in any case and production inputs will adapt to the only technique available (there is of course nothing in the framework of the surplus approach to guarantee that all the inputs will be fully utilised). For the neoclassical theory, on the contrary, regarding k as exogenous makes it impossible to arrive at an equilibrium distribution and prices. In point of fact, except by chance, k will not coincide with the exogenous endowments of K and L, which will give rise to a permanent imbalance between the firms’ demand for factors of production and the available supply of the same. We know, however, that the task preformed by prices and distributive variables in the neoclassical framework is precisely to bring demand into equilibrium with the given supply. In this case, however, k is fixed and the firms’ demand cannot therefore adapt to endowments. It is thus impossible to restore equilibrium and the prices and distributive variables cannot be determined

Impossibility · Advanced Thermodynamics and Statistical Mechanics · Economic theories and models · Economic Theory and Policy

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